Let’s go through each translation one by one.
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Problem 1: Trapezoid ABCD — translate 2 units left and 9 units up
First, find the original coordinates of points A, B, C, D from the graph:
- A is at (0, -2)
- B is at (2, -5)
- C is at (-5, -5)
- D is at (-3, -2)
Now apply the translation:
→ 2 units left → subtract 2 from x-coordinate
→ 9 units up → add 9 to y-coordinate
So for each point:
- A’ = (0 - 2, -2 + 9) = (-2, 7)
- B’ = (2 - 2, -5 + 9) = (0, 4)
- C’ = (-5 - 2, -5 + 9) = (-7, 4)
- D’ = (-3 - 2, -2 + 9) = (-5, 7)
✔ Check: The shape should look the same, just moved. Original was near bottom center; new one should be near top left. Makes sense.
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Problem 2: Trapezoid WXYZ — translate 7 units right and 1 unit down
Original coordinates:
- W is at (2, 1)
- X is at (2, 6)
- Y is at (-1, 5)
- Z is at (-1, 1)
Translation:
→ 7 units right → add 7 to x
→ 1 unit down → subtract 1 from y
New points:
- W’ = (2 + 7, 1 - 1) = (9, 0)
- X’ = (2 + 7, 6 - 1) = (9, 5)
- Y’ = (-1 + 7, 5 - 1) = (6, 4)
- Z’ = (-1 + 7, 1 - 1) = (6, 0)
✔ Check: Moved far right and slightly down. Looks correct.
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Problem 3: Parallelogram JKLM — translate 8 units right and 5 units up
Original coordinates:
- J is at (-1, 0)
- K is at (-4, -2)
- L is at (-8, -2)
- M is at (-5, 0)
Translation:
→ 8 right → +8 to x
→ 5 up → +5 to y
New points:
- J’ = (-1 + 8, 0 + 5) = (7, 5)
- K’ = (-4 + 8, -2 + 5) = (4, 3)
- L’ = (-8 + 8, -2 + 5) = (0, 3)
- M’ = (-5 + 8, 0 + 5) = (3, 5)
✔ Check: Moved far right and up. Shape preserved. Good.
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Problem 4: Parallelogram PQRS — translate 3 units left and 6 units down
Original coordinates:
- P is at (0, -3)
- Q is at (-3, 3)
- R is at (2, 3)
- S is at (5, -3)
Translation:
→ 3 left → -3 to x
→ 6 down → -6 to y
New points:
- P’ = (0 - 3, -3 - 6) = (-3, -9)
- Q’ = (-3 - 3, 3 - 6) = (-6, -3)
- R’ = (2 - 3, 3 - 6) = (-1, -3)
- S’ = (5 - 3, -3 - 6) = (2, -9)
✔ Check: Moved left and way down. All points shifted correctly.
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Final Answer:
The translated points are:
- Trapezoid ABCD → A’(-2,7), B’(0,4), C’(-7,4), D’(-5,7)
- Trapezoid WXYZ → W’(9,0), X’(9,5), Y’(6,4), Z’(6,0)
- Parallelogram JKLM → J’(7,5), K’(4,3), L’(0,3), M’(3,5)
- Parallelogram PQRS → P’(-3,-9), Q’(-6,-3), R’(-1,-3), S’(2,-9)
Parent Tip: Review the logic above to help your child master the concept of translations worksheet answer key.
